Water fountains are scattered throughout, and several are equipped specifically for filling bottles. I've easily filled bottles using even the ones not specially equipped -plenty of water pressure. And fyi, there are free sunscreen dispensers in every bathroom, so no need to worry about either of our desert enemies: dehydration or sunburn!
Yes, there are you can see them on the visitors map.
Yes. Clearly identified on the map.
Yes
Yes there is. Right outside the door of the curio shop.
Yes and I think they are also designated on the map
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